Mathematical Model of the Impact of Vaccination on the Transmission Dynamics of Fowl pox in Poultry

In this study, the researchers present the mathematical model of the impact of vaccination on the transmission dynamics of fowl pox in poultry. The model resulted in a system of 1st order ordinary differential equation. Analyzing the system using methods from dynamical system theory together with Routh-Harwitz theorem, it was established that the disease-free equilibrium is locally stable if the effective reproductive ratio Rρ = (1 - ρ) αβ/d1+r1+μ in the presence of vaccination is <1 and unstable if it is >1. Using the condition for control, the critical proportion that needs to be vaccinated to achieve herd immunity for fowl pox is established as ρc = αβ - (d1+r1+μ)/αβ. From this research, researchers discover that fowl pox can be eradicated from the poultry through vaccination provided the critical proportion ρc is achieved.